The iterative methods for solving nonlinear matrix equation X+A⋆X−1A+B⋆X−1B=Q

被引：0
|
作者：
Sarah Vaezzadeh
Seyyed Mansour Vaezpour
Reza Saadati
Choonkil Park
机构：
[1] Amirkabir University of Technology,Department of Mathematics and Computer Science
[2] Iran University of Science and Technology,Department of Mathematics
[3] Hanyang University,Research Institute for Natural Sciences
来源：
Advances in Difference Equations | / 2013卷
关键词：
nonlinear matrix equation; positive definite solution; inversion-free variant iterative method; convergence rate;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we study the matrix equation X+A⋆X−1A+B⋆X−1B=Q, where A and B are square matrices, and Q is a positive definite matrix, and propose the iterative methods for finding positive definite solutions of the matrix equation. Also, general convergence results for the basic fixed point iteration for these equations are given. Some numerical examples are presented to show the usefulness of the iterations.
引用
收藏
相关论文
共 50 条
  • [31] A numerical algorithm for solving the matrix equation AX + X T B = C 1
    Vorontsov, Yu. O.
    Ikramov, Kh. D.
    COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2011, 51 (05) : 691 - 698
  • [32] On positive definite solutions of the nonlinear matrix equation X+A☆X-n A = I
    El-Sayed, SM
    Al-Dbiban, AM
    APPLIED MATHEMATICS AND COMPUTATION, 2004, 151 (02) : 533 - 541
  • [33] ON THE NONLINEAR MATRIX EQUATION Xs + A*F(X)A = Q with s ≥ 1
    Zhou, Duanmei
    Chen, Guoliang
    Wu, Guoxing
    Zhang, Xiangyun
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2013, 31 (02) : 209 - 220
  • [34] Solving x-a=b(1)
    中学生数学, 2003, (12) : 41 - 41
  • [35] Newton's Iteration Method for Solving the Nonlinear Matrix Equation X+ Si=1mAi*X-1Ai=Q
    Li, Chang-Zhou
    Yuan, Chao
    Cui, An-Gang
    MATHEMATICS, 2023, 11 (07)
  • [36] The symmetric solutions of the matrix equation A1X1B1+A2X2B2+ •••+A1X1B1=C and its optimal approximation
    Peng Zhuo-hua
    Hu Xi-yan
    Zhang Lei
    ADVANCES IN MATRIX THEORY AND APPLICATIONS, 2006, : 135 - 138
  • [37] ON THE NONLINEAR MATRIX EQUATION X + Σi=1m Ai* X-q Ai = Q(0 < q ≤ 1)
    Yin, Xiaoyan
    Wen, Ruiping
    Fang, Liang
    BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2014, 51 (03) : 739 - 763
  • [38] 方程（x+a）1/2±（x+b）1/2=c解的探讨
    赵国林
    中学数学杂志, 1986, (03) : 19+7 - 19
  • [39] On the nonlinear matrix equation Xp = A#t(MT (X-1 + B)-1 M)
    Lee, Hosoo
    Meng, Jie
    LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (02): : 250 - 263
  • [40] Fixed-point accelerated iterative method to solve nonlinear matrix equation X - Σi=1mAi*X-1Ai = Q
    Li, Tong
    Peng, Jingjing
    Peng, Zhenyun
    Tang, Zengao
    Zhang, Yongshen
    COMPUTATIONAL & APPLIED MATHEMATICS, 2022, 41 (08):
12345